Outlier

Definition

An outlier lies unusually far from the other values, typically more than 1,5 interquartile ranges beyond the first or third quartile. Outliers distort the mean but not the median.

Worked example

In 4; 5; 6; 7; 42 the value 42 is an outlier.

Box-and-whisker check: Q1 = 12 and Q3 = 20, so IQR = 8 and 1,5 × IQR = 12. The limits are 12 − 12 = 0 and 20 + 12 = 32, so any value above 32 is an outlier.

Where it appears in the exam

Paper 2 statistics asks you to identify outliers from a box-and-whisker plot or data set and explain their effect on the mean and median.

Step-by-step method

1. Find Q1, Q3 and the IQR = Q3 − Q1.
2. Calculate Q1 − 1,5 × IQR and Q3 + 1,5 × IQR.
3. Any value outside these limits is an outlier.
4. Explain that an outlier pulls the mean but barely affects the median.

Common mistake

Using the range instead of the interquartile range to test for outliers.

Related statistics terms

• Standard deviation
• Least squares regression line
• Correlation coefficient

Frequently asked questions

What does outlier mean in Grade 12 Maths?

An outlier lies unusually far from the other values, typically more than 1,5 interquartile ranges beyond the first or third quartile. Outliers distort the mean but not the median.

Which NSC paper tests outlier?

Outlier belongs to the Statistics section of CAPS Grade 12 Mathematics, which is examined in Paper 2.

How do I practise questions involving outlier?

Snap a question that uses outlier into the Snap&Learn AI solver, or work through the statistics topic guide and NSC past papers.